Adventure Play sells an mp3 player for $18.00 and charges $3.25 per song. King Music sells a player for $23.00 and charges $2.00 per song. For how many songs will the cost be the same?

Answer: 4

Explanation:

Translate the english language to mathematical (algebraic) language.

This implies to define the variables and translates the statements into equations.

1) Adventure Play sells an mp3 player for $18.00 and charges $3.25 per song.

Cost = price of the mp3 player + price each song * number of songs

Variables:

number of songs: n

price each son: $3.25

price of the mp3 player: $ 18.00

Cost: c (n), this means that the cost is a function of n.

c (n) = 18 + 3.25n

2) King Music sells a player for $23.00 and charges $2.00 per song. For how many songs will the cost be the same?

Using the same procedure used for Adventure Play case:

c (n) = 23 + 2n

3) Equal cost = >

18 + 3.25n = 23 + 2n

=> 3.25n - 2n = 23 - 18

=> 1.25n = 5

=> n = 5 / 1.25

=> n = 4

Answer: the cost will be the same for 4 songs.